### On unitarily invariant ensembles of infinite Hermitian matrices

Mathematical Physics Seminar

5th October 2018, 2:00 pm – 3:00 pm

Howard House, 4th Floor Seminar Room

The unitarily invariant probability measures on infinite Hermitian

matrices have been classified by Olshanski and Vershik. In their work,

and another work by Borodin and Olshanski, the authors prove the almost

sure convergence of the renormalized extreme eigenvalues of the minors

when the dimension goes to infinity. In this talk, I present these

results, and another convergence result on eigenvectors I have recently proven.

These results apply in particular to the image of the Circular Unitary Ensemble by the Cayley transform which maps the

unit circle to the real line.

*Biography:*

See https://www.bristolmathsresearch.org/seminar/joseph-najnudel/ for full listing

*Organiser*: Nick Jones

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